Partially Altruistic Players in ( w ,τ)-strategic form non-cooperative games

We introduce a model of non-cooperative individuals with partially altruistic behaviour, called (w,τ)-strategic form game. Each individual has a target to reach and supports the social wellbeing using the strategies allowed by his target. So, the behaviour of individuals is between being fully selfish and being fully altruistic. An equilibrium of such a model, called (w,τ)-equilibrium, is a strategy profile where each individual cannot improve the social wellbeing using unilateral deviations allowed by his target. We give examples that illustrate the (w,τ) and compare it with previous altruistic equilibrium concepts. Finally, we provide sufficient conditions for the existence of (w,τ)-equilibria.